Objective Solve equations in one variable that contain variable terms on both sides.

Example 1: Solving Equations with Variables on Both Sides Solve 5 - n – 2 = 6. 3 – n = 6 To collect the variable terms on one side, subtract 2 from 5. –3 -3 -n = 3 3 is hanging on, so subtract 3 from both sides. Since -n is negative, divide both sides by -1. -1 -1 n = -3

Example 1: Solving Equations with Variables on Both Sides Solve 7n – 2 = 5n + 6. 7n – 2 = 5n + 6 To collect the variable terms on one side, subtract 5n from both sides. –5n –5n 2n – 2 = 6 + 2 + 2 2n = 8 Since n is multiplied by 2, divide both sides by 2 to undo the multiplication. n = 4

Check It Out! Example 1a Solve 4b + 2 = 3b. 4b + 2 = 3b To collect the variable terms on one side, subtract 3b from both sides. -3b –3b b + 2 = 0 – 2 – 2 b = –2

Check It Out! Example 1b Solve 5 - 3y = -7y + 3. To collect the variable terms on one side, add 4y to both sides. 5 - 3y = -7y + 3 + 7y + 7y 5 + 4y = 3 Since 5 is added to 4y, subtract 5 from both sides to undo the addition. -5 -5 4y = -2 4 4 Since y is multiplied by 4, divide both sides by 4 to undo the multiplication. y = -½

Check It Out! Example 1b Solve 2 + 4y = 9y – 8. To collect the variable terms on one side, subtract 4y from both sides. 2 + 4y = 9y – 8 –4y –4y 2 = 5y – 8 Since 8 is subtracted from 5y, add 8 to both sides to undo the subtraction. +8 +8 10 = 5y Since y is multiplied by 5, divide both sides by 5 to undo the multiplication. 2 = y

Check It Out! Example 2b Solve -2x + 15 + 1 = 2(x + 2). -2x + 15 + 1 = 2(x + 2) Distribute 2 to the expression in parentheses. -2x + 15 + 1 = 2(x) + 2(2) -2x + 15 + 1 = 2x + 4 -2x + 16 = 2x + 4 Combine like terms. +2x +2x To collect the variable terms on one side, add 2x to both sides. 16 = 4x + 4 – 4 – 4 Subtract 4 from both sides Divide by 4 and simplify. 12 = 4x 3 = x

Example 2: Simplifying Each Side Before Solving Equations Solve 12 – 6a + 4a = –1 – 5(7 – 2a). 12 – 6a + 4a = –1 –5(7 – 2a) Distribute –5 to the expression in parentheses. 12 – 6a + 4a = –1 –5(7) –5(–2a) 12 – 6a + 4a = –1 – 35 + 10a 12 – 2a = –36 + 10a Combine like terms. To collect the variable terms on one side, add 2a to both sides. Since –36 is added to 10a, add 36 to both sides. + 2a +2a 12 = -36 + 12a +36 +36 48 = 12a

Example 2 Continued Solve 4 – 6a + 4a = –1 – 5(7 – 2a). 48 = 12a 12 12 Since a is multiplied by 12, divide both sides by 12. 4 = a